Rick Santorum and Ron Paul battled for second place, while Newt Gingrich ran a distant fourth.
Romney's victory came on the heels of twin primary triumphs over Santorum earlier in the week in hard-fought Michigan and lightly contested Arizona, as well as a narrow win over Paul in Maine caucuses earlier in February.
Returns from caucuses in 43 percent of Washington state's precincts showed Romney with 37 percent of the vote, while Paul and Santorum each had 24 percent. Gingrich was drawing 11 percent.
There were 40 delegates at stake, and a likelihood that at least two of the contenders for the nomination to oppose President Barack Obama would add to their totals.
Romney, the former Massachusetts governor, had 173 delegates at the beginning of the day, according to an Associated Press count that includes party officials who will vote on the selection of a nominee but are not selected at primaries or caucuses. Santorum had 87, Gingrich 33 and Paul 20. It takes 1,144 delegates to win the nomination at the Republican National Convention this summer in Tampa.
The Republican race has shared the political spotlight in the past few days with a controversy in which conservative talk show host Rush Limbaugh called a Georgetown University law student a "slut" and a "prostitute" - an issue that the GOP presidential rivals seemed reluctant to comment on.
Limbaugh apologized on his website during the evening to the woman, Sandra Fluke, who had spoken out publicly in favor of a requirement for most insurance coverage to include contraception.
Romney, Santorum and Gingrich were all campaigning in Ohio - the most intensely contested of the Super Tuesday states - as the first caucus returns were reported.
Romney criticized Obama after a woman attending a campaign rally in Beavercreek said she had a daughter stationed in Afghanistan who believes the U.S. mission there is unclear. The woman also asked when Romney would bring the troops home.
"If your daughter is not familiar with the mission that she's on, how in the world can the commander in chief sleep at night, knowing that we have soldiers in harm's way that don't know exactly, precisely, what it is that they're doing there," the former Massachusetts governor said.
He said he'd bring troops home "as soon as humanly possible - as soon as that mission is complete."
Romney also said he would seek the repeal of legislation that passed Congress in 2002 to tighten accounting standards in the wake of the collapse of Enron and an ensuing scandal that cost shareholders millions of dollars.
Santorum spent the day in Ohio, where he touted his plan to improve the nation's manufacturing base and said part of the effort must include a reduction in the number of children born out of wedlock. In Cincinnati, the former Pennsylvania senator said there's less freedom in neighborhoods "where there are no dads."
While polls show him in a close race with Romney in the state, it is not clear he can fully convert any success in the primary into delegate strength. There are 76 delegates at stake in Ohio, of which 48 will be allocated, three at a time, to the winners of the state's 16 congressional districts. Santorum has only 30 of the 48 delegate slots filled for those contests.
Gingrich also campaigned in Ohio and drew laughs when he recalled what a voter in Tennessee had told him recently about rising gasoline prices. He said the man had said Obama has his own version of former candidate Herman Cain's 9-9-9 plan: "He wants us to pay $9.99 a gallon."
The former House speaker has said he must notch a Super Tuesday win in Georgia, where he launched his political career, but says he also has a chance to pick up delegates in Ohio.
Ron Paul was in Washington state as the caucuses began, searching for his first victory of the campaign.
It was a quirk in the campaign calendar that made Washington's caucuses the relatively low-key event that they were, sandwiched between a high-stakes clash between Romney and Santorum in Michigan and next-up primaries and caucuses in 10 states with 419 delegates at stake.
Of the 10, Ohio is the crown jewel, a big industrial state where Romney and Santorum maneuvered for their next showdown, and where Gingrich said he hopes to pick up a few delegates as well.
Apart from Ohio and Georgia, there also are primaries in Massachusetts, where Romney was governor, and Virginia, where Gingrich and Santorum failed to qualify for the ballot. Other primaries are in Tennessee, Oklahoma and Vermont.
Alaska, North Dakota and Idaho have caucuses.
